A Feasibility Analysis at Signal-Free Intersections (2403.05739v1)

Abstract: In this letter, we address the problem of improving the feasible domain of the solution of a decentralized control framework for coordinating connected and automated vehicles (CAVs) at signal-free intersections as the traffic volume increases. The framework provides the optimal trajectories of CAVs to cross the intersection safely without stop-and-go driving. However, as the traffic volume increases, the domain of the feasible trajectories decreases. We use concepts of numerical interpolation to identify appropriate polynomials that can serve as alternative trajectories of the CAVs, expanding the domain of the feasible CAV trajectories. We provide the conditions under which such polynomials exist. Finally, we demonstrate the efficacy of our approach through numerical simulations.

• The paper introduces a numerical interpolation framework using higher-order polynomials to expand the feasible trajectory domain for CAVs at signal-free intersections.
• It employs a double integrator dynamics model and a two-level optimization to compute energy-optimal and jerk-minimized trajectories, even in high-density traffic.
• Simulation results from MATLAB and PTV VISSIM validate the approach by reducing computational costs and overcoming cubic trajectory limitations for improved safety.

Feasibility Analysis at Signal-Free Intersections

Introduction

The paper "A Feasibility Analysis at Signal-Free Intersections" (2403.05739) explores the challenges and solutions associated with the coordination of Connected and Automated Vehicles (CAVs) at intersections without traditional traffic signals. The focus is on enhancing the domain of feasible solutions for decentralized control, especially under increasing traffic volumes. The research leverages numerical interpolation techniques to propose alternative and feasible trajectories for CAVs, allowing them to navigate intersections efficiently without stop-and-go movement, even in high-density traffic scenarios.

Problem Formulation

The core challenge addressed in the paper is the reduction of the feasible trajectory domain for CAVs as traffic volume rises. CAVs within a control zone must safely cross intersections devoid of signals without stopping. The current control framework limits the solution to a cubic trajectory, which becomes overly restrictive under congestion. The authors introduce a numerical interpolation approach employing higher-order polynomials to address this limitation, facilitating trajectory determination in real-time.

Figure 1: Schematic of the intersection showing the control zone, conflict points, and paths.

The vehicular dynamics model is a double integrator framework where safety constraints such as rear-end and lateral collision avoidance are imposed. To compute energy-optimal trajectories, the paper formulates two-level optimization problems where the first level seeks the shortest exit time, and the second level determines the optimal control inputs under state and traffic constraints.

Enhancing Feasible Solutions

This section presents the numerical interpolation framework for expanding the feasible solution domain. The foundational theorems guarantee unique polynomial solutions for given nodes and define conditions for matrix invertibility critical for interpolation. Specifically, the paper establishes criteria under which fourth-order polynomial trajectories can be derived, ensuring broader applicability even in dense traffic situations.

The theoretical presentation is supplemented with practical implementation guides for CAVs. It emphasizes the possibility of reducing jerk in trajectories—a critical aspect for optimizing energy and passenger comfort—while maintaining adherence to collision avoidance and vehicular constraints. The paper argues the solution's efficiency, showcasing its application in real-time trajectory planning for vehicles entering intersections.

Numerical Simulations

The paper validates the proposed framework through simulations conducted using MATLAB and PTV VISSIM software. The results demonstrate successful trajectory planning in scenarios previously unresolved by conventional cubic polynomial methods.

Figure 2: CAV trajectories defined only from Problem 2.

Figure 3: CAV trajectories defined from both Problem 2 and 3.

The distinct advantage of the interpolation method becomes evident as newly calculated trajectories reveal extended feasibility domains. The simulation outcomes show that a higher-order polynomial solution effectively accommodates increased vehicle density, reducing real-time computational costs while improving traffic flow and safety at intersections.

Conclusion

This research paper contributes significantly by addressing the limitations of existing decentralized control frameworks in signal-free intersections. The novel use of polynomial interpolation to broaden the feasible solution domain represents a pivotal advancement for CAV traffic management. Future research directions include applying these methodologies to more complex traffic systems and mixed traffic environments, ensuring widespread applicability and robustness of automated vehicular systems in diverse urban settings.